Inspired by the recent observation of a narrow resonance-like structure around 2360 MeV in the pn → dπ0π0 cross section, the possibility of forming a NN*(1440) quasi-molecular state is investigated by using a meson exchange model in which the π, σ, ρ and ω exchanges in t- and u-channels are considered. By adopting the coupling constants extracted from the relevant NN scattering and N*(1440) decay data, it is found that a deuteron-like quasi-molecular state of NN*(1440) with a binding energy in the range of 2 ∼ 67 MeV can be formed. Therefore, it is speculated that the observed structure around 2360 MeV might be or may have a large component of the NN*(1440) quasi-molecular state.